Feng Xiong PhD Professor of Civil Engineering Sichuan University Nonlinear Finite Element Analysis for Precast Short Column Connections Under Cyclic Loading

Background and Motivation P03P03 Seismic Behavior Testing of Precast short columns P04P04 Finite Element Analysis of Precast Short Columns P 18 Comparing of Shear Strength Formulas of Precast Column Joint between Chinese and Japanese Codes P 37 Conclusion P 39 CONTENTS

Background and Motivation  With the development of industrialized building, precast concrete structures are currently applied since the advantages in low costing, better quality, and quickly constructing;  The short columns with shear-span ratio less than 2.0 frequently occur in high-rise precast concrete frame structures with increasing of column section size;  The one concern in precast column design is the shear strength of joints in the column bottom. Does the shear failure occur along the joints when using wet connections, i.e. sleeve grouting connection?  In the new Chinese "Technical specification for precast concrete structures”(JGJ ), a shear strength formula is first given. But it is quite different from in Japanese codes

NoConcrete pouringRebar connectingJoint configuration PSC-A-1Cast-in-placeNoNo joint PSC-D-2Cast-in-placeSleeve groutingNo joint PSC-E-3PrecastSleeve groutingJoint with shear key PSC-C-4PrecastSleeve grouting Joint filled in grouting material PSC-B-6PrecastSleeve groutingJoint filled in concrete Two cast-in-place short columns and three precast short columns were tested under cyclic loading to investigate the effects of sleeve grouting connection and joint configurations on the behaviors of the column 。 Seismic Behavior Testing of Precast Short Columns Testing Objective Test specimens

Specimen PSC-A-1Specimen PSC-D-2 Testing specimen elevations

Specimen PSC-E-3Specimen PSC-C-4Specimen PSC-B-6 Testing specimen elevations

（ 1 ） Concrete NoConcrete Age （ day ） Cube Strength f cu （ MPa ） Cuboid Strength f c (MPa) PSC-A-1 C PSC-D PSC-E PSC-C PSC-B Materials of testing specimen （ 2 ） Steel rebar Diameter Yield strength fy(MPa) Ultimate strength fst(MPa) Elastic modulus Es(MPa) Remarks 18(1) In member PSC-D-2 、 PSC-E-3 、 PSC-C-4 、 PSC-B-6 18(2) In member PSC-A Stirrups

Testing Equipment

Loading System  The design axial compression ratio of all testing specimens is 0.6. The axial loads calculated as the measured concrete strength were exerted as the table following ；  Horizontal cyclic loading was controlled by the displacement as the figure. Specimen Axial Compression Calculated kN Axial Compression Exerted kN PSC-A PSC-D PSC-E PSC-C PSC-B

Testing process and observation Horizontal bending cracks occurred on the top ； When loading at displacement of±5.25m, diagonal cracks occurred in the cross shape ； When getting to ultimate loading, diagonal cracks distributed in whole column ； When loading at displacement of ±21mm concrete began to crush ； Finally loading at displacement of±42mm, concrete crushed and rebar exposed ， indicated column damage. Crack at mm Crack at 5.25mm Crack at 10.5mm to ultimate loading Crack at 42mm when damaging Specimen PSC-A-1 (cast in place)

Horizontal bending cracks occurred on the top at ±1.3125mm, with the joint at the bottom cracking ； Similar process occurred as the cast in place specimen ； Finally loading at displacement of±42mm, concrete crushed and rebar exposed ， but the joint crack didn’t go through. Cracking at mm Diagonal cracks occurred at 5.25mm At 10.5mm Got to ultimate loading At 42mm Specimen damaged Specimen PSC-E-3 (Precast) Testing process and observation

Hysteretic Curves PSC-A-1 PSC-D-2PSC-E-3 PSC-C-4 PSC-B-6 5 specimens including cast-in- place and precast columns have the similar hysteretic behavior and energy absorbed.

Skeleton curve Comparing with PSC- A-1and PSC-D-2 ， it is indicated that the sleeve has few effects on initial stiffness. With loading increases, the stiffness of sleeve column (PSC-D-2) decreases but ultimate strength increases. There is a longer platform at ultimate strength to slow down the stiffness degrading. PSC-A-1 vs PSC-D-2 Sleeve effects

Comparing with PSC-E-3 and PSC- C-4, it shows that the specimen with shear key has lower strength but better deformation and slower stiffness degrading than the specimen with the smooth joint. PSC-E-3 vs PSC-C-4 Shear key effect Skeleton curve

Comparing with PSC-C-4 and PSC-B-6 ， it shows that the specimen filled in high- strength grouting material in the joint has higher strength but less deformation than the specimen filled in concrete in the joint. PSC-C-4 vs PSC-B-6 Grouting material effect Skeleton curve

Ultimate Strength Nof c (MPa)V u + (kN)V u - (kN)V u + /f c bh 0 V u - /f c bh 0 Failure PSC-A Shear PSC-D Shear PSC-E Shear PSC-C Shear PSC-B Shear It is shown that the precast specimens have the similar strength and failure modes as the cast-in-place specimens.

Testing Conclusion  The rebar connected by the sleeve can insure the loading transfer, and the sleeve has no bad effect on the columns;  The precast columns using three horizontal joint configurations have the similar seismic behavior as the cast-in-place columns ；  Since the limit specimens, the shear behavior and failure mode along the joints can not be obtained. The test just proves that the precast column has the behavior equal to cast-in-place column.  To investigate if the shear failure occurs along the joint for precast short columns, numerical analysis is employed.

Finite Element Analysis of Precast Short Columns Attaching the material property Concrete: Damaged plastic model Reinforcement: Bi-linear model Finite element modeling Modeling components as the dimension

Finite Element Modeling 1. 划分网格，指定单元类型。 Defining interface and assembling each component TieTie (Cast-in-place) or Friction contact (Precast) Embedded region Specifying boundary condition EncastreConstraining Z translation and three rotations Exerting loadings Loading Finite element modeling Modeling components as the dimension Attaching the material property

Meshing and specifying element Concrete: three-dimensional linear brick elements Reinforcement: truss elements Finite element modeling Finite Element Modeling Defining interface and assembling each component Specifying boundary condition Exerting loadings Modeling components as the dimension Attaching the material property

Verifying the finite element model Taking the PSC-A-1 as a example. When observing the equivalent plastic tension strain （ PEEQT ）， it shows the process of“bending cracks occurring—diagonal cracks occurring—diagonal cracks developing— damaging in shear mode” ， and has a good agreement with the testing observation 。 mm5.25mm10.5mm42mm （1）Failure process and mode

The contact elements specified in the interface of joint indicates that cracks occurred along the joints of specimens PSC-E-3 、 PSC-C-4 、 PSC-B-6, but didn’t go through the joints. It states that the damage was not resulted by the shear sliding of the joints and agrees with the test observation. （ 2 ） Cracking in the joints of precast column PSC-E-3PSC-C-4PSC-B-6 Verifying the finite element model

（3）Skeleton Curves Verifying the finite element model Since the sleeve and shear key are not modeled In order to simplify the numerical analysis, a few errors can be observed from numerical results.

（4）Ultimate Strength SpecimenPSC-A-1PSC-D-2PSC-E-3PSC-C-4PSC-B-6 Testing （ kN ） FE results （ kN ） Relative Errors （ % ） Testing （ kN ） FE results （ kN ） Relative errors （ % ） Testing （ kN ） FE results （ kN ） Relative errors （ % ） Verifying the finite element model The comparing between numerical analysis and testing results indicates that the finite element models work well. It can be used to stimulate the precast short columns

Parameter Analysis To extend the test study, finite element parameter analysis is conducted. For precast short columns the two important parameters to effect joint shear behaviors are the axial compression ratio and shear-span ratio. By use of the verified model, 9 numerical models are defined as the changes of axial compression ratio and shear-span ratio. Modelshear-span ratio Column height（mm） axial compression ratio Axial compression （kN） n n n n n n n n n

Equivalent plastic strain Comparing of columns with fixed shear-span ratio of 1.5 and different axial compression ratios n n n With the decrease of axial compression ratio, the plastic strains increases and implies that cracks develop quickly and damages occur early.

n n n With the decrease of shear-span ratio, the cracks occur from the middle column and develop diagonally in a cross shape. But the final failure modes are similar and all in the shear damage. Equivalent plastic strain Comparing of columns with fixed axial compression ratio of 0.6 and different shear-span ratios

Joint states at failure stage n n n n n n n n n When the axial compression ratio changes from 0.6 to 0.3, no sliding is observed along the bottom joints. It indicates that precast columns fail as the cast- in-place columns; When axial compression ratio decreases to 0.1, the obvious sliding occurs along the joints. The failure of precast column is resulted by Insufficient shear strength of joints. The failure belongs to connection failure.

Rebar stresses at failure stage n n n Stirrups yield but vertical rebar is in low stress when columns damage. It indicates that the column damage is the shear failure and dowel action of rebar through joints doesn’t indicate. Stirrups and rebar through the joint yield. The column damage comes from the shear failure of the joint.

Hysterical Curves  When axial compression ration decreasing to 0.1, the deformation decreases and the areas covered by hysterical curve decrease. It implies that the shear damage of joint is less ductile than shear damage of whole column.

 With the decrease of shear-span ratio, the stiffness increases but plastic deformation decreases.  Under low axial compression ratio and shear-span ratio （ n ）， joint sliding occurs in the first loading cycle. Hysterical Curves

Skeleton curves  The ultimate strength decreases with the axial compression ratio deceasing. The ultimate deformation under axial compression ratio of 0.1 is more less than that of 0.3 to 0.6

 Under the same axial compression ratio, the ultimate strength increases and deformation capacity decreases with the shear-span decreasing. Skeleton curves

Ultimate strength

The ultimate strength deceases with the axial compression ratio deceasing; and increases with the shear-span ratio deceasing. Ultimate strength

Numerical analysis conclusion  The axial compression ratio is the key factor to effect the shear failure of joints. It decides if the precast short column fails in the connection or in the column self equal to the cast-in-place column.  For the precast short columns the shear failure will occur along the joints when the axial compression ratio is low, i.e The failure is very brittle with less deformation. Therefore when designing the precast short columns with low axial compression ratio, it is necessary to check the shear capacity for the joints.  The shear-span ratio affects the initial stiffness, deformation ability and ultimate strength for precast short columns. With the decrease of shear- span ratio, the initial stiffness and ultimate strength will enhanced, but deformation will reduce.

Comparing of Shear Strength Formulas of Precast Column Joint between Chinese and Japanese Codes Japanese codeChinese code Shear resistance from friction along joint ： Shear resistance from rebar dowel action force ： Friction coefficient ： Area of dowel rebar ： Tensile rebar is neglected 。 Friction coefficient ： 0.8 for all Area of dowel rebar ： All the rebar through the joint is considered.

Calculating the shear strength of 9 models as the Chinese code and Japanese code respectively （taking the same friction coefficient of 0.8）, the results are shown in the table following： No. Axial compressi on ratio Shear- span ratio Numerical results(kN) Calculations as Japanese code(kN) Calculations as Chinese code(kN) n n n n n n n n n Comparing of Shear Strength Formulas of Precast Column Joint between Chinese and Japanese Codes When axial compression ratios are 0.3 and 0.6, the calculation results are higher than numerical predictions for two codes. It indicates that the failure occurs in the columns. When axial compression ratio is 0.1, Japanese code has a good agreement with numerical results.

Conclusion  The test of 5 specimens indicates that the precast columns with wet connections have the similar strength, deformation and Energy consumption ability as the cast-in-place columns.  Numerical analysis indicates that shear failure occurs along the joint when axial compression is low. This damage is very brittle with less deformation. To avoid the shear failure along the joint, the shear strength of horizontal joints has to be checked when designing.  By comparing with Chinese code and Japanese code of precast structures, the shear strength formula of Chinese code is overestimate by considering both contact friction and rebar dowel action together.

THANKS 谢谢聆听